Authors:

Antonio Mezzacapo(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

Guillermo Romero(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

Laura Garc\'Ia-\'Alvarez(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

Jorge Casanova(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

Lucas Lamata(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

Enrique Solano(Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain)

In this contribution, we present the quantum simulation of fermionic field modes interacting via a continuum of bosonic modes with superconducting circuits. Unlike many quantum technologies, superconducting circuits offer naturally the continuum of bosonic modes by means of one-dimensional transmission lines. In particular, we consider a simplified version of 1+1 quantum electrodynamics (QED), which may describe Yukawa interactions, and the coupling of fermions to the Higgs field. Our proof-of-principle proposal is designed within the state-of-the-art circuit QED technology, where fermionic fields are encoded in superconducting flux qubits, in a scalable approach that may lead to a full-fledged quantum simulation of quantum field theories.